1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Number Theory: Unique Numbers

  1. May 17, 2014 #1
    Does anyone know of a reference work that lists natural numbers with unique properties? Like 26, for example, being the only natural number sandwiched between a square (25) and a cube (27). Does such a reference book exist?


    IH
     
  2. jcsd
  3. May 17, 2014 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Wikipedia has such information: http://en.wikipedia.org/wiki/38_(number [Broken])
     
    Last edited by a moderator: May 6, 2017
  4. May 17, 2014 #3
    Thanx Micro, I was aware of certain Wikipedia articles; what I specifically am looking for though, is a systematic reference work of all know unique numbers. I could not find something resembling this on the net...
     
  5. May 17, 2014 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    It depends a lot on the things you consider as unique properties. Every number has unique properties, but most of them are boring ("is the only number x where x-23 and x-24 are primes" is another one for 26). Random collections are the best things you can find.
     
  6. May 17, 2014 #5
    Hmm...is that a trivial uniqueness quality that you just mentioned for 26? Doesn't seem so to me but then I am the layman here...

    Can one somehow 'define' mathematical triviality for such unique qualities I wonder...


    IH
     
  7. May 17, 2014 #6

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    It is trivial in the way that "x-23 prime and x-24 prime" requires two primes with a difference of just 1, and 2 and 3 are the only primes that satisfy this.
    You can set this up for every integer.
     
  8. May 17, 2014 #7
    Yes, if course...silly me...
     
  9. May 18, 2014 #8

    Curious3141

    User Avatar
    Homework Helper

  10. May 18, 2014 #9
    Thanx Curious, exactly the type of thing I was looking for, thanx a million...I kept repeating "unique" in all my Google searches, so there you go...a little variety is always good...


    IH
     
  11. May 18, 2014 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Note that not all those entries are unique, and some of them just reflect our limited knowledge. And some are... pointless.

    "151 is a palindromic prime." - true, but there are 7 smaller palindromic primes and probably infinitely more larger ones.
    "146 = 222 in base 8." - so what?
     
  12. May 19, 2014 #11
    Thanx for the clarification mob...funny I would have thought that a compendium of numbers with unique characteristics would be a given in number theory...quite surprised that it's so difficult to find...


    IH
     
  13. May 21, 2014 #12
    Last edited by a moderator: May 6, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Number Theory: Unique Numbers
  1. Number Theory (Replies: 7)

  2. Number theory (Replies: 2)

  3. Number Theory (Replies: 1)

Loading...